The paper presents a method to estimate the frequencies of a multi-harmonic signal in finite time. We use parameterization based on applying delay operators to a measurable signal. The result is a linear regression model with an unknown vector which depends on the signal parameters. We use Dynamic Regressor Extension and Mixing method to replace the n-th order regression model with scalar regressions. After that, we estimate the parameters separately using the standard gradient descent method. In the last step, we find algebraically the finite-time parameter estimates. The set of numerical simulations demonstrates the efficiency of the proposed approach.